Many vehicles today include stability control systems that improve a vehicle's handling. Vehicle stability control systems typically use a means for determining a driver's intended vehicle path when providing stability control to the vehicle. A driver's intended vehicle path can be determined by calculating a yaw gain using parameters such as a vehicle speed and a desired road-wheel angle, which is the driver's hand-wheel angle divided by a steering gear ratio. The yaw gain then can be used to calculate a steady state yaw rate, which can in turn be used to calculate a steady state lateral velocity and, hence, determine a driver's intended vehicle path.
Typically, such vehicle stability control system calculations rely upon an approximate representation of steering geometry defined by Equation 1 below:
                    δ        =                              L            R                    +                                    K              u                        ⁢                          a              y                                                          (                  Equation          ⁢                                          ⁢          1                )            In Equation 1, δ represents a vehicle road wheel angle, L represents a wheelbase of the vehicle, R represents a turn radius of the vehicle, Ku represents a vehicle understeer gradient (namely, a measure of the vehicle's tendency to “understeer” during a turn, which occurs when a circular path of the vehicle's motion during the turn has a larger diameter than a circular path indicated by a direction in which the vehicle's road wheels are pointed), and ay represents a vehicle lateral acceleration. Equation 1, which is commonly referenced in the literature, is based on an assumption that the turn radius is much larger than the wheelbase and that the steer angles are small, so that small angle simplifications can be used, such as the arc tangent of an angle being equal to the angle.
Most vehicle stability control methods and systems today rely upon parameters calculated using Equation 1 above. For example, values obtained from Equation 1 are often used to calculate a yaw rate and a yaw gain for the vehicle in accordance with Equation 2 and Equation 3 below:Ω=ay/Vref  (Equation 2)Ωg=Ω/δ  (Equation 3)In Equations 2 and 3, Ω represents a yaw rate of the vehicle, Vref represents a velocity of the vehicle, and Ωg represents a yaw gain. The yaw rate and the yaw gain are typically utilized as parameters for use in controlling steering of the vehicle, for example in controlling various actions of an electronic stability control system of the vehicle. Specifically, the yaw gain is typically used to calculate a steady-state value for the yaw rate, which in turn is used in controlling one or more steering actions, for example of an electronic stability control system of the vehicle.
While such control methods and systems today may be quite accurate when a vehicle's turn radius is significantly larger than the vehicle's wheelbase, they are more limited when the turn radius is not significantly larger than the wheelbase. For example, during tight turning maneuvers, reliance on the approximations inherent in Equation 1 above may result in less than optimal accuracy.
Accordingly, it is desired to provide improved methods, systems, and programs for calculating a yaw gain for use in controlling a vehicle, particularly in situations when the turn radius is not significantly larger than the wheelbase, for example during tight turning maneuvers. Furthermore, other desirable features and characteristics of the present invention will be apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and the foregoing technical field and background.